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Module 1: Advanced Algebraic Expressions

Topics Covered:

1. Review of Basics from Beginner Level
2. Multiplication and Division of Algebraic Expressions
3. Simplifying Complex Expressions
4. Exponents and Powers

Practice Questions:

1. Simplify: 2x⋅(3x+4)2x \cdot (3x + 4)2x⋅(3x+4).
2. Simplify: 6x23x\frac{6x^2}{3x}3x6x2​.
3. If a=2a = 2a=2 and b=3b = 3b=3, evaluate (a2b+b2a)(a^2b + b^2a)(a2b+b2a).

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Module 2: Linear Equations in Two Variables

Topics Covered:

1. Understanding Linear Equations with Two Variables
2. Graphical Representation
3. Solving Linear Equations using Substitution and Elimination Methods

Practice Questions:

1. Solve: 2x+y=72x + y = 72x+y=7 and x−y=1x – y = 1x−y=1 using substitution.
2. Represent the equation x+2y=6x + 2y = 6x+2y=6 on a graph.
3. Solve using elimination: 3x+4y=103x + 4y = 103x+4y=10 and 5x−4y=65x – 4y = 65x−4y=6.

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Module 3: Quadratic Equations

Topics Covered:

1. General Form of Quadratic Equations
2. Methods of Solving Quadratic Equations
   • Factorization
   • Completing the Square
   • Quadratic Formula
3. Nature of Roots (Discriminant Analysis)

Practice Questions:

1. Solve: x2−5x+6=0x^2 – 5x + 6 = 0x2−5x+6=0 using factorization.
2. Find the roots of x2+4x+4=0x^2 + 4x + 4 = 0x2+4x+4=0 using the quadratic formula.
3. Determine the nature of roots for x2−2x+1=0x^2 – 2x + 1 = 0x2−2x+1=0.

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Module 4: Polynomials

Topics Covered:

1. Division of Polynomials
2. Remainder Theorem and Factor Theorem
3. Zeros of a Polynomial and Their Relationship with Coefficients

Practice Questions:

1. Divide 2×3+3×2−x−22x^3 + 3x^2 – x – 22×3+3×2−x−2 by x−1x – 1x−1.
2. Use the Remainder Theorem to find the remainder when x3−4x+2x^3 – 4x + 2×3−4x+2 is divided by x−2x – 2x−2.
3. Find the zeros of x2−3x+2x^2 – 3x + 2×2−3x+2.

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Module 5: Inequalities

Topics Covered:

1. Linear Inequalities in Two Variables
2. Solving and Graphing Inequalities
3. Systems of Inequalities

Practice Questions:

1. Solve: 2x+3>72x + 3 > 72x+3>7.
2. Graph the inequality x+y≤5x + y \leq 5x+y≤5 on a Cartesian plane.
3. Solve the system of inequalities: x+y≤5x + y \leq 5x+y≤5, x−y≥1x – y \geq 1x−y≥1.

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Module 6: Sequences and Series

Topics Covered:

1. Arithmetic Progression (AP)
   • General Term and Sum of Terms
2. Geometric Progression (GP)
   • General Term and Sum of Terms
3. Applications of Progressions

Practice Questions:

1. Find the 10th term of the AP: 3,7,11,…3, 7, 11, \dots3,7,11,….
2. Find the sum of the first 15 terms of the GP: 2,4,8,…2, 4, 8, \dots2,4,8,….
3. Determine whether 3,6,12,24,…3, 6, 12, 24, \dots3,6,12,24,… is an AP or a GP.

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Module 7: Matrices and Determinants (Introduction)

Topics Covered:

1. Basics of Matrices
   • Types of Matrices (Row, Column, Square, Zero, Identity)
2. Operations on Matrices
   • Addition, Subtraction, Scalar Multiplication
3. Determinants of 2×2 Matrices

Practice Questions:

1. Add the matrices:
   A=[1234]A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}A=[13​24​] and B=[201−1]B = \begin{bmatrix} 2 & 0 \\ 1 & -1 \end{bmatrix}B=[21​0−1​].
2. Find the determinant of [2314]\begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}[21​34​].
3. Multiply 333 by the matrix [1−205]\begin{bmatrix} 1 & -2 \\ 0 & 5 \end{bmatrix}[10​−25​].

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Module 8: Coordinate Geometry

Topics Covered:

1. Distance Formula
2. Midpoint and Section Formula
3. Equation of a Line
   • Slope-Intercept Form, Point-Slope Form, Two-Point Form

Practice Questions:

1. Find the distance between the points (2,3)(2, 3)(2,3) and (5,7)(5, 7)(5,7).
2. Determine the midpoint of the line segment joining (−1,4)(-1, 4)(−1,4) and (3,−2)(3, -2)(3,−2).
3. Write the equation of the line passing through (1,2)(1, 2)(1,2) with a slope of 333.

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Module 9: Functions and Relations

Topics Covered:

1. Definition of Functions and Relations
2. Domain and Range
3. Types of Functions
   • Linear, Quadratic, Polynomial

Practice Questions:

1. Identify the domain and range of f(x)=2x+3f(x) = 2x + 3f(x)=2x+3.
2. Determine whether the relation R={(1,2),(2,3),(3,4)}R = \{(1, 2), (2, 3), (3, 4)\}R={(1,2),(2,3),(3,4)} is a function.
3. Graph f(x)=x2f(x) = x^2f(x)=x2.

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Module 10: Final Review and Comprehensive Test

Topics Covered:

1. Revision of Key Concepts
2. Mixed Questions on All Topics
3. Real-Life Applications of Algebra

Mock Test Sample Questions:

1. Solve: x2+7x+10=0x^2 + 7x + 10 = 0x2+7x+10=0.
2. Simplify: 2×2+4x2x\frac{2x^2 + 4x}{2x}2x2x2+4x​.
3. Solve the inequality: x−3>2x – 3 > 2x−3>2.
4. Find the distance between (0,0)(0, 0)(0,0) and (4,3)(4, 3)(4,3).
5. Determine the slope of a line passing through (2,5)(2, 5)(2,5) and (6,9)(6, 9)(6,9).

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Additional Materials

• Worksheets with Higher Difficulty Questions
• Concept Recap PDFs
• Quizzes after each module
• Project: Solve a real-world problem using algebra (e.g., financial planning, travel optimization).

This syllabus builds on the foundational topics and introduces intermediate concepts, making it suitable for learners progressing in algebra.

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